Time: 10:00-11:30 a.m. Place: Jeffery Hall 319
Speaker: Jamie Mingo (Queen's University)
Title: Fully Matricial Functions, Part II.
Abstract: I will discuss the difference-differential calculus.
Time: 10:00-11:30 a.m. Place: Jeffery Hall 319
Speaker: Jamie Mingo (Queen's University)
Title: Tensor Products of Modules and Vector Spaces.
Abstract: This talk will review the construction of the tensor product of modules and its universal property. This property can be used to establish associativity, commutativity over direct sums, and a check for linear independence when our modules are vector spaces. I also hope to give a brief introduction to tensor norms.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Sang-Gyun Youn (Queen's University)
Title: Some questions on Jones-Wenzl projections in view of quantum information theory.
Abstract: It is very natural to study separability or PPT property of quantum states in view of quantum information theory and the need to study those properties for so-called Jones-Wenzl projections has emerged in recent years. In this talk, I am going to introduce the notions of separability, PPT property and Jones-Wenzl projections.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Jamie Mingo (Queen's University)
Title: A-valued laws, II
Abstract: We will continue the discussion from last week and show an analytic representation of A-valued laws.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Josué Vázquez-Becerra (Queen's University)
Title: Direct sums and Tensor products of Hilbert Bi-modules
Abstract: Direct sums and Tensor products of Hilbert Bi-modules
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Pei-Lun Tseng (Queen's University)
Title: Right Hilbert A-modules, Part II
Abstract: For the last talk, we gave some motivating examples and the definition of right A-module. We will begin this talk by showing some properties of A-valued pre inner product, and then we will deduce the process to construct a right Hilbert A-module. Next, we will introduce the operators on right Hilbert A-modules, and proving some properties of the corresponding adjoint operators.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Pei-Lun Tseng (Queen's University)
Title: Right Hilbert A-modules
Abstract: Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Pei-Lun Tseng (Queen's University)
Title: A-Valued Theory
Abstract: In order to study operator-valued probability, we need some basic knowledge of C*-algebras. In this talk, I am trying to review what is a C*-algebra. and some properties of C*-algebras. The GNS construction will be covered, which is known as the follows: every C*-algebras can be represented as a algebra of bounded linear operators on a Hilbert space. This construction gives us good starting point to study matrices over a C*-algebra. If time permits, I will introduce right Hilbert A-modules.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Jamie Mingo (Queen's University)
Title: Additive Convolution and Subordination
Abstract: Last week I reviewed the basic facts of scalar free independence. This week I will continue with a new convolution of probability measures called the free additive convolution. We will use a tool from complex analysis called subordination to get our convolution. It will then lead to a discussion of conditional expectation which will be the basis of operator valued freeness.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Jamie Mingo (Queen's University)
Title: I will begin by reviewing the basic facts of scalar free independence
Abstract: This fall the seminar will be a learning seminar with lectures by (willing) participants. The theme will be operator valued freeness. This is the non-commutative version of conditional independence, now we have independence over a subalgebra. In many cases the subalgebras are n x n matrices so this is quite a general situation.
I will begin by reviewing the basic facts of scalar free independence. The seminar will follow a recent book by D. Kaliuzhnyi-Verbovetskyi and V. Vinnikov and some lecture notes of D. Jekel.
